(untitled) (Analysis in Theory and Applications, 2017)
Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z)=nP(z)+(α-z)P'(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.